Green Function approach is more physical?

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SUMMARY

The discussion centers on the preference for the Green function approach over dimensional regularization in deriving the Casimir energy for a massless scalar field, as presented in Milton's 'The Casimir Effect'. Participants express a consensus that Green functions provide a more intuitive and physically meaningful framework compared to dimensional regularization, which involves complex dimensions that lack clear physical interpretation. The conversation highlights the perceived superiority of Green functions in the physics community, particularly in the context of regularization techniques.

PREREQUISITES
  • Understanding of quantum field theory concepts, particularly the Casimir effect.
  • Familiarity with dimensional regularization techniques.
  • Knowledge of Green functions and their applications in physics.
  • Basic grasp of propagators in quantum mechanics.
NEXT STEPS
  • Research the application of Green functions in quantum field theory.
  • Study the implications of dimensional regularization in particle physics.
  • Explore the physical interpretations of propagators in quantum mechanics.
  • Investigate alternative regularization methods and their comparative advantages.
USEFUL FOR

The discussion is beneficial for theoretical physicists, quantum field theorists, and students interested in advanced regularization techniques and their physical interpretations.

robousy
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Hey folks,

I'm not really sure which forum to put this question in but I figured this was probably the best as it deals with issues of regularization.

I'm reading Miltons 'The Casimir Effect'. In chapter one he derives the Casimir energy for a massless scalar field by employing dimensional regularization. He then goes on in the next section to derive the same result using a Green function approach which he claims is "...a physical and rigorous approach".

From this sentence it appears that he favors the Green function approach over Dim reg. Is this a general 'feeling' in the physics community? That Green functions are somehow superior to Dim Reg? Also, why should this be 'physical'?

I hope this question makes sense.

Rich
 
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I do have the feeling that Greens functions are more physical than dimensional regularization. That is, I can very well imagine the physical meaning of a propagator, but I don't really have intuition for 4 + \epsilon dimensions with \epsilon \in \mathbb{C}.
I can't remember seeing Greens functions being used for regularization though.
 

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